The Minnesota Constitution states that the size of the Legislature must be prescribed by law, therefore the Legislature determines the size of the Legislature (Minnesota Constitution, Article IV - Legislative Department).
The Minnesota Legislature has 67 senators and 134 representatives for a total of 201 members. The size of the Legislature has changed over time. Since statehood the lowest number of members was 63 and the highest was 202. The House Public Information Office's Minnesota State Government Series: State Lawmakers goes into more detail about the number of legislators and the size of legislative districts.
Legislative district lines are redrawn every ten years, following the decennial U.S. Census. Each state uses the census data to draw its legislative boundaries. The courts have held that each district must be nearly equal in population size. In Minnesota, and in most other states, the Legislature is charged with redistricting. For information about other states, please see NCSL: Creation of Redistricting Commissions.
No matter who is charged with the task of drawing district boundaries, the final product often is challenged in court. Once in the judicial system, the plan must meet strict criteria for approval. Redistricting plans have been ruled invalid for many reasons, including gerrymandering (creating oddly shaped districts to create a partisan advantage), compacting (concentrating voters of a single political persuasion into as few districts as possible), and fracturing (spreading voters of a single political persuasion among many districts to dilute their collective voting strength).
To learn more about redistricting, visit the comprehensive redistricting web page from the Legislative Coordinating Commissions Subcommittee on Geographic Information Systems Office (GIS). The GIS office also has an option to download a PDF of current district maps. There is additional information about redistricting in the Redistricting Guides from the Legislative Reference Library.